I am Jim Fowler.

Jim Fowler is a mathematician at The Ohio State University. His research interests broadly include geometry and topology, and more specifically focus on the topology of high-dimensional manifolds and geometric group theory. In other words, he thinks in depth about highly symmetric geometric objects. He's fond of using computational techniques to attack problems in pure mathematics.

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Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. This online course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.

Sequences and Series will challenge us to think very carefully about "infinity." What does it mean to add up an unending list of numbers? How can an infinite task result in a finite answer? These questions lead us to some very deep concepts—but also to some powerful computational tools which are used not only in math but in many quantitative disciplines.

This course is a first introduction to sequences, infinite series, convergence tests, and Taylor series. It is suitable for someone who has seen just a bit of calculus before.

M2O2C2 is an invitation to think carefully about how one thing changing affects something else. What is the "derivative" of a function of many variables? How can a curved object be approximated by a flat plane? What does the chain rule look like when many things are affecting many other things? How do we find an input which maximizes a function of many variables?

This is a course in multivariable differential calculus, but we will also introduce a ton of linear algebra. The result is a course targeted at a student who has seen a bit of calculus and is willing to learn about matrices and vectors to provide the best possible vantage point from which to understand derivatives of functions of many variables.